Question: The grades on a history midterm at Almond are normally distributed with $\mu = 68$ and $\sigma = 5.5$. Nadia earned a $58$ on the exam. Find the z-score for Nadia's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Nadia's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{58 - {68}}{{5.5}}} $ ${ z \approx -1.82}$ The z-score is $-1.82$. In other words, Nadia's score was $1.82$ standard deviations below the mean.